Variable Star Light Curves in Koopman Space

TL;DR

This paper applies Koopman theory-based data-driven techniques to analyze variable star light curves, revealing differences in eigenvalue complexity between RRc and RRab stars and observing eigenvalue changes over time related to the Blazhko effect.

Contribution

It introduces a novel application of Koopman spectral analysis to variable star light curves, providing a new method for classification and understanding of stellar variability.

Findings

RRc stars summarized by ~8 eigenvalues, RRab by ~12

Eigenvalues differ between star subclasses, indicating structural differences

Eigenvalue changes over time suggest physical insights into the Blazhko effect

Abstract

We present the first application of data-driven techniques for dynamical system analysis based on Koopman theory to variable stars. We focus on light curves of RRLyrae type variables, in the Galactic globular cluster $\omega$ Centauri. Light curves are thus summarized by a handful of complex eigenvalues, corresponding to oscillatory or fading dynamical modes. We find that variable stars of the RRc subclass can be summarized in terms of fewer ($\approx 8$) eigenvalues, while RRab need comparatively more ($\approx 12$). This result can be leveraged for classification and reflects the simpler structure of RRc light curves. We then consider variable stars displaying secular variations due to the Tseraskaya-Blazhko effect and find a change in relevant eigenvalues with time, with possible implications for the physical interpretation of the effect.